An integral transport theory calculation of neutron flux distributions in rectangular lattice cells

An integral transport theory method is described for calculating the flux distribution in an infinite, rectangular lattice, assuming mono-energetic neutrons and isotropic scattering. Important features of the method are: the rectangular cell boundary is treated exactly and the contribution of the surrounding cells to the reference cell is included explicitly.

The method is implemented in a computer program, CELTIC, and a description is given of the numerical techniques used by the program to solve the singular integral equation. The convergence and accuracy of CELTIC is assessed by a comparison with exact analytic results which are obtainable for the spatially constant cross section case.

Fluxes and disadvantage factors for the well-known Thie lattices are computed by CELTIC and compared with the results obtained by previous workers who used various transport techniques most of which rely on the cylindricalized cell approximation. The increase in accuracy resulting from the use of ‘White’ boundary conditions rather than the reflecting boundary condition in the cylindricalized cell is demonstrated.

The variation of the disadvantage factor, ξ, as a function of the cell volume/fuel volume ratio is studied as the cell width decreases until the fuel region becomes the inscribed circle, for the case that the neutron cross sections remain unchanged. A minimum in the ξ curve is found, which confirms the result obtained in a previous paper which, however, assumed spatially constant neutron cross sections in the square cell.